Problem7174--ABC272 —— E - Add and Mex

7174: ABC272 —— E - Add and Mex

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Time Limit : 1.000 sec  Memory Limit : 256 MiB

Description

You are given an integer sequence $A=(A_1,A_2,\ldots,A_N)$ of length $N$.
Perform the following operation $M$ times:
  • For each $i\ (1\leq i \leq N)$, add i to $A_i$. Then, find the minimum non-negative integer not contained in $A$.

Input

The input is given from Standard Input in the following format:
$N\ M$
$A_1\ A_2\ \ldots\ A_N$

Output

Print $M$ lines.
The i-th ($1\leq i \leq M$) line should contain the minimum non-negative integer not contained in A after the i-th operation.

Constraints

$1≤N,M≤2×10^5$
$-10^9\leq A_i\leq 10^9$
All values in the input are integers.

Sample 1 Input

3 3
-1 -1 -6

Sample 1 Output

2
2
0

The 1-st operation makes the sequence A

(-1 + 1, -1 +2 ,-6+3) = (0,1,-3).

The minimum non-negative integer not contained in A is 2.

The 2-nd operation makes the sequence A

(0 + 1, 1 +2 ,-3+3) = (1,3,0).

The minimum non-negative integer not contained in A is 2.

The 3-rd operation makes the sequence A

(1 + 1, 3 +2 ,0+3) = (2,5,3).

The minimum non-negative integer not contained in A is 0.

Sample 2 Input

5 6
-2 -2 -5 -7 -15

Sample 2 Output

1
3
2
0
0
0

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